We all know that maths is really hard. So hard, in fact, that there’s literally a whole Wikipedia page dedicated to unsolved mathematical problems, despite some of the greatest minds in the world working on them around the clock.

But as Avery Thompson points out at Popular Mechanics, from the outset at least, some of these problems seem surprisingly simple – so simple, in fact, that anyone with some basic maths knowledge can understand them… including us. Unfortunately, it turns out that proving them is a little harder.

Prime numbers are those magical unicorns that are only divisible by themselves and 1. As far as we know, there’s an infinite number of primes, and mathematicians are working hard to constantly find the next largest prime number.

But is there an infinite amount of prime numbers pairs that differ by two, like 41 and 43? As primes get larger and larger, these twin primes are harder to find, but in theory, they should be infinite… the problem is no one’s been able to prove that as yet.

This is something most of us have struggled with before – you’re moving into a new apartment and trying to bring your old sofa along. But, of course, you have to maneuver it around a corner before you can get comfy on it in your living room.

Rather than giving up and just buying a beanbag, at this point, mathematicians want to know: what’s the largest sofa you could possible fit around a 90 degree corner, regardless of shape, without it bending? (Although they’re looking at the whole thing from a two-dimensional perspective.)

“The largest area that can fit around a corner is called – I kid you not – the sofa constant.

Nobody knows for sure how big it is, but we have some pretty big sofas that do work, so we know it has to be at least as big as them. We also have some sofas that don’t work, so it has to be smaller than those. All together, we know the sofa constant has to be between 2.2195 and 2.8284.”

The Collatz conjecture is one of the most famous unsolved mathematical problems, because it’s so simple, you can explain it to a primary-school-aged kid, and they’ll probably be intrigued enough to try and find the answer for themselves.

So here’s how it goes: pick a number, any number.

If it’s even, divide it by 2. If it’s odd, multiply it by 3 and add 1. Now repeat those steps again with your new number. Eventually, if you keep going, you’ll eventually end up at 1 every single time (try it for yourself, we’ll wait).

As simple as it sounds, it actually works. But the problem is that even though mathematicians have shown this is the case with millions of numbers, they haven’t found any numbers out there that won’t stick to the rules.

“It’s possible that there’s some really big number that goes to infinity instead, or maybe a number that gets stuck in a loop and never reaches 1,” explains Thompson. “But no one has ever been able to prove that for certain.”

Similar to the Twin Prime conjecture, Goldbach’s conjecture is another seemingly simple question about primes and is famous for how deceptively easy it is. The question here is: is every even number greater than 2 the sum of two primes?

It sounds obvious that the answer would be yes, after all, 3 + 1 = 4, 5 + 1 = 6 and so on.

But, again, no one’s been able to prove that this will always be the case, despite years of trying.

The reality is that, as we continue to calculate larger and larger numbers, we may eventually find one that isn’t the sum of two primes… or ones that defy all the rules and logic we have so far. And you can be sure mathematicians aren’t going to stop looking until they find it.